40 Invention of the fpiral Gunfer^ s Rule. 



VIII. 



Account of the original Invention of the circular Injirument for performing Calculations on ihf 

 Principle of Gunter's Rule made by Clairault le Plre, and communicated to the Royal 

 Academy of Sciences in the Tear 1727*. (W. N.) 



I 



N the firft volume of thij Journal, page 372, I gave ^n account, with drawings, of a 

 fpiral inftrument confilling of a combination of the fe£tor and Gunter's rule, equivalent to 

 an ordinary rule of forty feet in length, which had been communicated by me to the 

 Royal Society about thirteen years ago, as my own invention. In the paper here referred 

 to, I did juftice to George Adams the father, who, as I afterwards difcovered, had con- 

 trived and made a very powerful inftrument of the fame kind in 1748, fince prefented to 

 me by his fon. The fame principles of candour and juftice call upon me at prefent to 

 afcribe the original thought, as well as the actual mechanical conftrudtion, to the elder 

 Clairault ; of whofe engraving, publilhed twenty-one years before the date of Adams's 

 manufcript, I have here given a copy. An abridged account of his paper will fhew that 

 he was well aware of the properties and advantages of this apparatus. 



He begins by obferving that the beft expedients for the folution of right lined triangles 

 are reducible to linear conftru£tion, or logarithmic calculations ; that the firft, by means 

 of the feftor, requires much Ikill, to produce a moderate degree of accuracy : while the 

 latter demands a certain quantity of refearch and computation, which render it defirabJe to 

 Cmplify the procefs. With this intention he propofed to unite thefe two excellent dif- 

 coverles which he performed by placing all the logarithms diftindlly on the furface of a 

 circle of twenty-one inches in diameter, upon concentric circumferences ; marking not 

 only the natural numbers as far as ten thoufand, but alfo the fines of the degrees and 

 minutes. The figure in plate i reprefents a twelfth part of the circular inftrument, and" 

 the external fliaded branches denote the feftor between which the intervals are meafured. 

 In the year 1716, the author executed his firft fyftcm on a fquare of one foot, filled with 

 parallel lines, conftituting altogether a rule of 1500 French feet: and it was not till the 

 year 1720 that he thought of the fpiral form. But as this fet of lines, when numerous, 

 prefented fome difficulties, principally, as I fuppofe, from the difficulty of marking and 

 counting the intervals upon the blades of the feQor, he gave the preference to concentric 

 circles. I need not enter into the minute particulars of the conftrudion, becaufe this has 

 been already done in our Journal, and in the Philofophical Tranfa£llons. He does not 

 overlook the advantage (which alfo occurred to me) of this ftrufture that it affords by the 

 enlargement of the external arcs, a remedy for the fmallnefs of the differences in certain 

 parts of the logarithmic lines. 



The learned writer concludes his paper by giving fome numerical examples of its ufe 



and application. 



* Machines approvees par I'Acad. Roy. tome V. 



